Conditional Nonlinear Optimal Perturbation Method Reveals Optimal Precursors of El Niño in a Data-Driven Climate Model

Gradient-based explainable artificial intelligence (XAI) methods identify input features that locally influence weather and climate forecasts, but their reliance on linearization limits their ability to characterize finite-amplitude perturbations that evolve through nonlinear dynamics. More importantly, such methods are not naturally suited to counterfactual questions such as: what initial perturbation can optimally trigger a specific climate event? Here, we introduce an event-oriented conditional nonlinear optimal perturbation (CNOP) framework into WalkerNet, an autoregressive model of global ocean-atmosphere fields, to identify optimal precursors of El Niño events. Specifically, sea surface temperature (SST) and sea surface height (SSH) perturbations are jointly optimized through a 12-month nonlinear rollout under a prescribed relative $L_2$ constraint. The optimization objective combines a delayed-onset penalty during the early forecast stage with maximization of Niño 3.4 index growth during the mature stage. This temporal constraint prevents the optimization from trivially generating El Niño by directly warming the Niño 3.4 region at initialization, requiring instead that the event emerge through the subsequent nonlinear evolution of the coupled system. We apply the framework to multiple naturally evolving cases simulated by WalkerNet and optimize CNOPs that promote the development of El Niño. The optimized perturbations consistently induce substantial El Niño development, while their spatiotemporal evolution exhibits physically interpretable structures consistent with established ENSO mechanisms. These results demonstrate that CNOP provides a nonlinear counterfactual XAI framework for discovering dynamically meaningful optimal precursors of climate events, connecting forecast sensitivity, precursor identification, and event-level interpretation in AI-based Earth system models.